FoCM 2014 conference

Workshop A1 - Computational Dynamics

December 11, 17:00 ~ 17:25 - Room B21

Coexistence of hexagons and rolls

Jean-Philippe Lessard

Université Laval, Canada   -

In this talk we introduce a rigorous computational method for finding heteroclinic solutions of a system of two second order differential equations. These solutions correspond to standing waves between rolls and hexagonal patterns of a two-dimensional pattern formation PDE model. After reformulating the problem as a projected boundary value problem (BVP) with boundaries in the stable/unstable manifolds, we compute the local manifolds using the Parameterization Method and solve the BVP using Chebyshev series and the radii polynomial approach. Our results settle a conjecture by Doelman et al. about the coexistence of hexagons and rolls.

Joint work with Jan Bouwe van den Berg (VU Amsterdam), Andréa Deschênes (Laval) and Jason Mireles James (Rutgers).

View abstract PDF